423 articles – 192 references  [version française]

hal-00675045, version 3

Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring

Sorina Ionica (http://www.loria.fr/~ionica/) 1

  • 1:  CARAMEL (INRIA Nancy - Grand Est / LORIA)

  • INRIA – CNRS : UMR7503 – Université de Lorraine France
  • Available versions :  v1 (2012-02-29) v2 (2012-03-29) v3 (2012-04-20) v4 (2013-05-02)

    • Bibliographic reference

    • Type of document: Documents without publication reference (Preprint)
    • Subject: Mathematics/General Mathematics
    • Title: Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
    • Abstract: Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the $\ell$-Tate pairing in terms of the action of the Frobenius on the $\ell$-torsion of the Jacobian of a genus 2 curve. We apply similar techniques to study the non-degeneracy of the $\ell$-Tate pairing restrained to subgroups of the $\ell$-torsion which are maximal isotropic with respect to the Weil pairing. First, we deduce a criterion to verify whether the jacobian of a genus 2 curve has maximal endomorphism ring. Secondly, we derive a method to construct horizontal $(\ell,\ell)$-isogenies starting from a jacobian with maximal endomorphism ring.
    • Fulltext language: English
    • Keyword(s): abelian variety – Tate pairing – Galois cohomology
    • ANR Project:
      Project Id ANR CHIC
      Year 2009
      Project acronyme CHIC
      Project title Courbes Hyperelliptiques, Isognénies, Comptage

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    • hal-00675045, version 3
    • http://hal.archives-ouvertes.fr/hal-00675045
    • oai:hal.archives-ouvertes.fr:hal-00675045
    • From: Sorina Ionica <>
    • Submitted on: Friday, 20 April 2012 18:15:54
    • Updated on: Friday, 20 April 2012 21:55:23